Ministers are considering exempting fully vaccinated NHS staff in slot xo England from having to self-isolate if they are traced as a Covid contact.
Health bosses have been urging the government to change the rules amid fears of staff shortages.
Sources said no decision had been taken and ministers wanted to see evidence the move would be safe.
If it goes ahead, self-isolation would be replaced with daily tests from 19 July, when wider curbs are eased.
The idea echoes a similar policy that would apply to all fully vaccinated people and children in England from 16 August.
It comes as medical leaders warn the Covid situation in the UK will get worse before it gets better with the NHS "under unprecedented pressure".
Saffron Cordery, deputy chief executive at NHS Providers which represents health trusts, said double-jabbed health service staff "should be able to carry on working even if they are pinged" by the NHS Covid-19 app.
She said: "The government should bring that in as soon as possible. I can't see any reason to delay. NHS trusts are struggling with the number of staff having to isolate - anecdotally we're seeing significant numbers off [work]."
"We've picked up on the fact some staff are deleting the app, but it's not happening on a big, widespread scale at this point."
Health and social care workers were among the first people in the UK to be eligible for a coronavirus vaccine when it became available in December 2020.
Of the estimated 1.3m NHS trust health care workers in England, around 1.1m have received two vaccine doses, according to data from NHS England.